Based on past James Cameron films, Avatar may have been shot in an aspect ratio similar to Super 35 (though, since it's all digital, it won't technically be "Super 35"). Here's how that works: http://en.wikipedia.org/wiki/Super_35. (I had to remove the T2 image since it wasn't showing up.)
You can see the comparisons on the right-hand side. The red box is the 2.39:1 theatrical frame, and the green box is the 1.33:1 home video "fullscreen" frame. Many of Cameron's films (The Abyss, T2, Titanic) were shot this way (Cameron himself has even said that he prefers the fullscreen versions of some of his Super 35 films, including T2, if I remember correctly).
It's my assumption, from everything that I've heard so far, that Avatar is being done one of two ways:
1) Shot full-aperture akin to Super 35, cropped differently for 2.39:1 or 1.78:1. Effects shots would likely be 1.78:1, cropped on top and bottom for 2.39:1.
2) Shot 1.78:1, cropped on top and bottom for 2.39:1 (also effects shots).
I say that it's likely that the effects shots are all natively 1.78:1 because it's simply cheaper that way. In the case of most Super 35 films (like T2), the effects shots are done in 2.39:1, and are panned and scanned like normal 2.39:1 films. So while you're getting more of the original image (in some cases) with the fullscreen version of Super 35 movies, you're getting the exact same cropping for the effects shots that you would if it wasn't shot in Super 35.
For Avatar, I'd say that #2 is probably more likely, simply because it would be easier and cheaper. This would mean the 3D showings are OAR, and the 2D showings are cropped for 2.39:1. Any fullscreen version would likely be cropped from the 1.78:1 version. Either way, since 60% of the movie is completely CGI, 1.78:1 is almost certainly the original intended aspect ratio.
And I have my ticket for Friday at 12:15 PM at the Chicago Navy Pier IMAX. I'll definitely post my thoughts after I see it.